Question

Below are several MRPS questions. Match the best answers to the question. However, I have left off the units for obvious reasons! For all problems, assume that positive x is to the right and positive y is upward.

A roller coaster cart starts at rest and speeds up at 3.8 m/s/s on a straight, level track for 1.9 s. Next, the cart slows down at 1.1 m/s/s for 0.5 s on the straight, level track, and then the cart travels at a constant velocity for another 2.3 s as it prepares to go up a hill. How far does the cart go while on this part of the ride?

Possible Answer choices

A.	7.0
B.	16
C.	24.8
D.	52.1
E.	3.5
F.	32.8
G.	40.1
H.	73.8
I.	13
J.	6.3
K.	45.8
L.	60.2
M.	14.5

Answer 1

here,

for time interval , t1 = 1.9 s

final speed , v1 = 3.8 m/s

let the acceleration be a1

v1 = u1 + a1 * t1

3.8 = 0 + a1 * 1.9

a1 = 2 m/s^2

the distance travelled , s1 = v1^2 / 2a1

s1 = 3.8^2 / (2*2) = 3.61 m

for time interval , t2 = 0.5 s

initial speed , u2 = 3.8 m/s

final speed , v2 = 1.1 m/s

let the acceleration be a2

v2 = u2 + a2 * t2

1.1 = 3.8 + a2 * 0.5

a2 = -5.4 m/s^2

the distance travelled be s2

v2^2 - u2^2 = 2 * a2 * s2

1.1^2 - 3.8^2 = 2 * (-5.4) * s2

s2 = 1.225 m

for t3 = 2.3 s

the distance travelled , s3 = v2 * t3

s3 = 1.1 * 2.3 m = 2.53 m

the total distance travelled , s = s1 + s2 + s3

s = 7 m

the total distance is A) 7 m